Question: Rewrite as a simplified fraction. ${3.89\overline{4} = {?}}$
Solution: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 3894.4444...\\ 100x &= 389.4444...\end{align*}}$ Subtracting the two equations, we have: ${900x = 3505}$ ${x = \dfrac{3505}{900}} $ ${x = \dfrac{701}{180}} \text{or} {3 \dfrac{161}{180}}$